A. R. Calderbank
E. G. Coffman
Abstract
Two mathematical models dealing with optimal placement of directories on disk devices are analyzed. Storage addresses on the disk are approximated by points in the interval [0, 1]. Requests for information on the disk are represented by a sequence of file names. To process a request, a read-write head is first moved to a directory kept on the disk that specifies the address of the file, and then a head is moved to the specified address. The addresses are assumed to be independent and uniform on [0,1].
In the first model we consider a system of two heads separated by a fixed distance d and a directory situated at 0 ≤ x ≤ 1. In the second model we consider a system consisting of one head and n ≥ 2 directories at 0 ≤ x1 < x2 < … < xn ≤ 1. For both models we study the problem of finding those values of the parameters that minimize the expected head motion to process a request in statistical equilibrium.
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Index Terms
- Optimal directory placement on disk storage devices
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